Laplace() R function from [nlmm]

The Laplace Distribution

Density, distribution function, quantile function and random generation for the (symmetric) Laplace distribution.


dl(x, mu = 0, sigma = 1, log = FALSE)
pl(x, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
ql(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rl(n, mu = 0, sigma = 1)

Arguments

x: vector of quantiles.
p: vector of probabilities.
n: number of observations.
mu: location parameter.
sigma: positive scale parameter.
log,log.p: logical; if TRUE, probabilities are log--transformed.
lower.tail: logical; if TRUE (default), probabilities are $P[X \le x]$ otherwise, $P[X > x]$ . Similarly for quantiles.

Details

The Laplace distribution has density

f(x) =\frac{1}{\sqrt{2}\sigma}e^{-\frac{\sqrt(2)}{\sigma} |x - \mu|}

where $\mu$ is the location parameter and $\sigma$ is the scale parameter. Note that based on this parameterization, the distribution has variance $\sigma^2$ .

Returns

dl gives the density and rl generates random deviates.

References

Kotz, S., Kozubowski, T., and Podgorski, K. (2001). The Laplace distribution and generalizations. Boston, MA: Birkhauser.

Author(s)

Marco Geraci

Laplace function